Question

A study of bone density on 5 random women at a hospital produced the following results. Age 37 45 57 61 65 Bone Density 350 345 340 320 315 Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.

Answer 1

SOLUTION:

From given data,

A study of bone density on 5 random women at a hospital produced the following results. Age 37 45 57 61 65 Bone Density 350 345 340 320 315 Step 3 of 3 : Calculate the correlation coefficient, r. Round your answer to three decimal places.

We have the data,

Age	37	45	57	61	65
Bone Density	350	345	340	320	315

Sample size = n = 5

Age (X)	Bone Density (Y)	X*Y	X2	Y2
37	350	12950	1369	122500
45	345	15525	2025	119025
57	340	19380	3249	115600
61	320	19520	3721	102400
65	315	20475	4225	99225
X = 265	Y = 1670	X*Y =87850	X2 =14589	Y2 =558750

The formula for  the correlation coefficient, r is

r =( n (∑ xy) − ( ∑x )( ∑y ) ) / sqrt( [ n ∑ x² − ( ∑x )² ][ n ∑ y² − ( ∑ y )²] )

By substituting all values from above table then we get,

r =( 5 (87850)− (265)(1670) ) / sqrt( [ 5 (14589) − (265)² ][ 5 (558750) − ( 1670)²] )

r = - 3300 / 3632.07929

r = - 0.90857

r = - 0.909 ( Rounded answer to three decimal places )